# Ch 55: 6th-8th Grade Algebra: Monomials & Polynomials

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### About This Chapter

## 6th-8th Grade Algebra: Monomials & Polynomials - Chapter Summary

In this chapter for 6th through 8th grade algebra students, video lessons teach how to define monomials and polynomials, how to complete basic mathematical operations as well as more complex problems (e.g. finding roots, working with several variables, graphing and more) with monomials and polynomials. These 10-minute-or-less videos include example problems to work through and lesson quizzes to fortify what students learn. Once students have finished the video lessons, they may take a chapter exam to assess what they learned.

## Chapter Lessons and Objectives

Lesson | Objective |
---|---|

What Are Monomials & Polynomials? | Instructors teach students what monomials and polynomials are and how to determine the degree of polynomials. |

How to Add & Subtract Monomials | This lesson shows students how to add and subtract monomials. |

How to Multiply & Divide Monomials | Instructors describe how to multiply and divide monomials. |

Square & Cube Roots of Monomials | Instructors demonstrate how to find the square and cube roots of monomials. |

How to Evaluate a Polynomial in Function Notation | This lesson teaches students how to evaluate polynomials in function notation. |

Understanding Basic Polynomial Graphs | The lesson shows how to graph first degree polynomials. |

Basic Transformation of Polynomial Graphs | Instructors describe basic transformations of polynomial graphs. |

How to Graph Cubics, Quartics, Quintics and Beyond | With this lesson, instructors demonstrate how to graph cubics, quartics, etc. |

How to Add, Subtract and Multiply Polynomials | The lesson shows how to add, subtract and multiply polynomials. |

Pascal's Triangle: Definition and Use with Polynomials | Instructors explain what the Pascal's Triangle is and how to use it. |

The Binomial Theorem: Defining Expressions | Instructors teach students about binomial expressions and the binomial theorem. |

How to Divide Polynomials with Long Division | In this lesson, example problems show how to divide polynomials using long division. |

How to Use Synthetic Division to Divide Polynomials | This lesson shows how to divide polynomials using synthetic division. |

Dividing Polynomials with Long and Synthetic Division: Practice Problems | The lesson examines students' abilities to use long and synthetic division when dividing polynomials. |

Operations with Polynomials in Several Variables | Instructors teach students how to perform mathematical operations with polynomials in multiple variables. |

### 1. What Are Monomials & Polynomials?

Watch this video lesson to learn about how coefficients and variables combine to form monomials and polynomials. You'll also learn how the exponent determines the degree of polynomials.

### 2. How to Add & Subtract Monomials

In this video lesson, you will learn what kinds of monomials you can add or subtract together. You will also learn how to immediately tell when you cannot add or subtract your monomials.

### 3. How to Multiply & Divide Monomials

In this lesson, we're going to learn how to multiply and divide monomials. As you can imagine, this is a very important skill that much of algebra (and even more advanced math) depends upon.

### 4. Square & Cube Roots of Monomials

Being able to find the cube or square root of monomials will make algebra, and indeed all math, much easier. However, it's not as hard as you'd think. This lesson will show you how and allow you to test your skills with a quiz.

### 5. How to Evaluate a Polynomial in Function Notation

This lesson will review how to evaluate polynomials in function notation. Along with an analogy to explain the process, examples will be given and worked during the lesson.

### 6. Understanding Basic Polynomial Graphs

This lesson will cover understanding basic polynomial graphs. The lesson focuses on how exponents and leading coefficients alter the behavior of the graphs.

### 7. Basic Transformations of Polynomial Graphs

The basic transformations for a graph are movement up and down, left and right, pinched or stretched graphs, and flipped graphs. This lesson will review how to accomplish each of these transformations.

### 8. How to Add, Subtract and Multiply Polynomials

Adding, subtracting and multiplying polynomials are, basically, the same as adding, subtracting and multiplying numbers. They only difference is that we have a pesky variable to worry about, but this video will show you that's no problem, so no worries! This method has worked for many of my students, and I think it will work for you, too!

### 9. Pascal's Triangle: Definition and Use with Polynomials

Pascal's Triangle is defined and discussed briefly. Following the introduction to the triangle, its use in expanding polynomial powers is elaborated with examples.

### 10. The Binomial Theorem: Defining Expressions

In this lesson, students will learn the binomial theorem and get practice using the theorem to expand binomial expressions. The theorem is broken down into its parts and then reconstructed.

### 11. How to Divide Polynomials with Long Division

Arithmetic long division and polynomial long division are very similar. Yes, it's a long process, but once you have the rhythm you will get every problem correct!

### 12. How to Use Synthetic Division to Divide Polynomials

Synthetic division is a 'short-cut' way of dividing a polynomial by a monomial. You still need to know long division, sorry, but this method is way fun when you're dividing by a monomial!

### 13. Dividing Polynomials with Long and Synthetic Division: Practice Problems

Let's look at some more polynomial division problems. We will use long division and synthetic division, but this time we will have a couple of more involved problems. So, get out some paper and a pencil and let's begin!

### 14. Operations with Polynomials in Several Variables

In this video lesson, you will learn how to handle and work with polynomials that have more than one variable. This is important because in math you sometimes have to work with several variables at the same time.

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### Other Chapters

Other chapters within the 6th-8th Grade Math: Practice & Review course

- 6th-8th Grade Math: Basic Arithmetic Operations
- 6th-8th Grade Math: Divisibility
- 6th-8th Grade Math: Properties of Numbers
- 6th-8th Grade Math: Number Theory
- 6th-8th Grade Math: Factoring
- 6th-8th Grade Math: Estimating & Rounding
- 6th-8th Grade Math: Whole Numbers
- 6th-8th Grade Math: Simplifying Whole Number Expressions
- 6th-8th Grade Math: Negative Numbers
- 6th-8th Grade Math: Absolute Value
- 6th-8th Grade Math: Integers
- 6th-8th Grade Math: Rational Numbers
- 6th-8th Grade Math: Inequalities
- 6th-8th Grade Math: Introduction to Decimals
- 6th-8th Grade Math: Operations with Decimals
- 6th-8th Grade Math: Introduction to Fractions
- 6th-8th Grade Math: Operations with Fractions
- 6th-8th Grade Math: Percents
- 6th-8th Grade Math: Exponents & Exponential Expressions
- 6th-8th Grade Math: Roots & Radical Expressions
- 6th-8th Grade Algebra: Writing Algebraic Expressions
- 6th-8th Grade Algebra: Basic Algebraic Expressions
- 6th-8th Grade Algebra: Algebraic Distribution
- 6th-8th Grade Algebra: Writing & Solving One-Step Equations
- 6th-8th Grade Algebra: Writing & Solving Two-Step Equations
- 6th-8th Grade Algebra: Simplifying & Solving Rational Expressions
- 6th-8th Grade Math: The Coordinate Graph
- 6th-8th Grade Algebra: Linear Equations
- 6th-8th Grade Algebra: Systems of Linear Equations
- 6th-8th Grade Math: Properties of Functions
- 6th-8th Grade Math: Graphing Functions
- 6th-8th Grade Math: Solving Math Word Problems
- 6th-8th Grade Measurement: Perimeter & Area
- 6th-8th Grade Geometry: Introduction to Geometric Figures
- 6th-8th Grade Geometry: Angles
- 6th-8th Grade Measurement: Units of Measurement
- 6th-8th Grade Geometry: Triangles
- 6th-8th Grade Geometry: Quadrilaterals
- 6th-8th Grade Geometry: Circles
- 6th-8th Grade Geometry: Circular Arcs & Measurement
- 6th-8th Grade Geometry: Polyhedrons & Geometric Solids
- 6th-8th Grade Geometry: Symmetry, Similarity & Congruence
- 6th-8th Grade Geometry: Transformations
- 6th-8th Grade Geometry: Triangle Theorems & Proofs
- 6th-8th Grade Geometry: Similar Polygons
- 6th-8th Grade Geometry: The Pythagorean Theorem
- 6th-8th Grade Math: Data & Graphs
- 6th-8th Grade Math: Probability
- 6th-8th Grade Math: Statistics
- 6th-8th Grade Math: Rates, Ratios & Proportions
- 6th-8th Grade Math: Money
- 6th-8th Grade Math: Consumer Math
- 6th-8th Grade Math: Number Sequences
- 6th-8th Grade Math: Sets